(November 26th, 2015)
In Section 40, I described my recent RX Antenna upgrade going from Single Yagis to a full 2x13 array. Shortly after setting up the 2x13 array, I was able to make several QSO's with very low ERP stations, which suggested that the improvement was real and significant. 
One obvious question I posed to myself was: How much performance advantage am I really getting out of this? We know that the maximum Forward Gain advantage going from let's say a 1X13 to a 2X13 is about 2.85 dB, so am I at least getting the theoritical improvement, more or less? In theory, the 2X13 should do a better job rejecting some noise so how much extra benefit does that amount to?
Obviously, this was a perfect case to employ the Moon Echo capability in order to attempt quantifying the performance advantage. I decided to conduct an experiment to compare the RX performance of the 1X13 versus the new 2x13 array. 
Here is the simple protocol I employed for the experiment:
1) Fix the polarity of the RX antenna(s) tested to 0 degree (HPOL)
2) Optimize the polarity of the TX Antenna Array (2X14 RPOL, 965 watts) in order to maximize the signal of the Echo Traces produced while RXing with the 2x13 array.
3) Produce and record the signals of 30 moon echos (RX antennas is 2x13).
4) Go outside and turned the 2x13 array into a 1x13 RX antenna, and rotate the de-activated antenna by 90 degrees so it does not interfere with the active 1x13.
5) Produce and record the signals of 30 moon echos (RX antenna is 1x13).
6) Switch the system back to a 2x13 array.
7) Produce and record the signals of 30 moon echos (RX antennas is 2x13).
After this experiment, we end up with 3 sets of 30 data points, 2 sets for the 2x13 array, and 1 set for the 1x13 antenna. The complete data is shown in the table to the right. The main reason to use the "sandwich" approach, i.e. testing 2X13, 1x13 and then 2x13 again, is to ensure that the base conditions/signals are not drifting too much during the overall experiment which took several minutes to conduct. One can imagine that Faraday Rotation alone could lead to a significant drift and bias the results of the experiment... The video of the entire experiment is also available below the table with some captions in order to describe what is taking place.
The results of the experiment are quite interesting. Here are the averages and measures of variance obtained from the 3 data sets recorded:
Antenna Average Variance
2x13 -24.1 dB 1.9 dB
1x13 -29.2 dB 1.8 dB
2x13 -24.5 dB 1.6 dB


First, the "sandwich" technique confirmed equivalent performance for the two separate tests done with the 2x13 array. This means that the conditions were stable and did not drift during the duration of the experiment.
It is also interesting to note that the standard deviations (std) calculated for each data set, which is a good measure of the signals variation, were quite similar and consistent. A basic statistical analysis showed that the data sets were normally distributed, so from a probability standpoint, if we round the variance to 2 dB, one can say that 68% of the time, the signal will vary by no more than +/- 2 dB, 95.5% of the time, by no more than +/- 4 dB, and 99.7% of the time, by no more than +/- 6 dB.  
In terms of Moon Echo strength, I have obtained much stronger echos in the past using a single 1x13 as RX antenna, but the EME conditions were what they were that day, so the key aspect for this experiment is that both antenna systems (1x13 and 2x13) were tested under the same conditions. If we average all the echos recorded with the 2x13, and compare to the 1x13 antenna, the overall RX performance improvement observed is 4.9 dB.
The 4.9 dB improvement figure is quite interesting since this number is much greater than the maximum theoritical 2.85 dB Forward Gain improvement. The greater figure is obviously mainly due to the improvement in terms of better noise rejection in favor of the 2x13 array (lower temperature). MAP65 showed a reduction in the noise floor by about 1dB with the 2x13 array. Note that the reduction may actually be more than that in reality where the effect of the bandpass filters is sensitive to the impedance of the antenna system being utilized so MAP65 noise floor reading is not totally representative in this case. If we use 1dB noise reduction as a starting point, we get ~ 2.85dB + 1.0 dB = 3.9 dB advantage. With a 2 dB noise reduction, the RX improvement would add up to 4.9 dB, which is exactly what was recorded during the experiment.
The experiment demonstrated that going from a 1x13 RX antenna to a 2x13 array provides an RX performance advantage in the order of 4-5 dB, which is significantly more than the maximum theoritical "Forward Gain" improvement of 2.85 dB. The Moon Echo capability (thanks to RPOL!) provides a very practical way to evaluate and make useful EME performance comparison using self-produced signals returned from the Moon.   
***WARNING: For Best Resolution, it is critical to select 720p HD resolution in the youtube "settings" at bottom right of the player. The 360p default setting won't yield good enough resolution to see the details. It will take several seconds before the High Resolution kicks in, so you will need to restart the video from the beginning when the High Resolution is active and select to view the video in "Full Screen Mode" for best experience...***